Estimating parameters of a model that is non-linear and is more complex than a log-linear model

Abstract

A method for estimating parameters of a model that is non-linear and is more complex than a log-linear model, the method may include feeding measured observations and sampling coordinates of the measured observations to a machine learning process; and processing the measured observations and the sampling coordinates of the measured observations, by the machine learning process, to provide an estimate of the parameters of the model; wherein the model is indicative of a relationship between the measured observations and the sampling coordinates.

We claim: 
     
         1 . A method for estimating parameters of a model that is non-linear and is more complex than a log-linear model, the method comprises:
 feeding measured observations and sampling coordinates of the measured observations to a machine learning process; and   processing the measured observations and the sampling coordinates of the measured observations, by the machine learning process, to provide an estimate of the parameters of the model; wherein the model is indicative of a relationship between the measured observations and the sampling coordinates.   
     
     
         2 . The method according to  claim 1  wherein the model is a multi-exponential model. 
     
     
         3 . The method according to  claim 1  wherein the model is a diffusion weighted magnetic resonance imaging model. 
     
     
         4 . The method according to  claim 1  wherein the machine learning process is trained during a training period in which the machine learning process is fed by training observations and training sampling coordinates. 
     
     
         5 . The method according to  claim 4  wherein some of the training sampling coordinates are generated by randomly biasing initial training sampling coordinates to provide randomly biased training sampling coordinates. 
     
     
         6 . The method according to  claim 5  wherein some of the training observations represent estimated training observations obtained at the randomly biased trained sampling coordinates. 
     
     
         7 . The method according to  claim 5  wherein some of the training observations are simulated. 
     
     
         8 . The method according to  claim 1  comprising training the machine learning during a training period, wherein the training comprises feeding the machine learning process by training observations and training sampling coordinates. 
     
     
         9 . The method according to  claim 8  comprising generating some of the training sampling coordinates by randomly biasing initial training sampling coordinates to provide randomly biased training sampling coordinates. 
     
     
         10 . The method according to  claim 9  comprising obtaining some of the training observations at the randomly biased trained sampling coordinates. 
     
     
         11 . The method according to  claim 9  wherein some of the training observations are simulated. 
     
     
         12 . The method according to  claim 1  comprising feeding the measured observations and sampling coordinates of the measured observations to an input stage of the machine learning process. 
     
     
         13 . The method according to  claim 1  wherein the machine learning process is implemented by a neural network. 
     
     
         14 . The method according to  claim 13  wherein the neural network is a feed-forward back-propagation deep neural network. 
     
     
         15 . The method according to  claim 13  wherein the neural network comprises multiple fully connected layers. 
     
     
         16 . The method according to  claim 1  wherein the machine learning process is trained by a supervised training process. 
     
     
         17 . The method according to  claim 1  wherein the machine learning process is trained by an un-supervised training process. 
     
     
         18 . The method according to  claim 1  wherein the machine learning process is trained by a combination of a supervised training process and an un-supervised training process. 
     
     
         19 . A non-transitory computer readable medium for estimating parameters of a model that is non-linear and is more complex than a log-linear model, the non-transitory computer readable medium comprises:
 feeding measured observations and sampling coordinates of the measured observations to a machine learning process; and   processing the measured observations and the sampling coordinates of the measured observations, by the machine learning process, to provide an estimate of the parameters of the model; wherein the model is indicative of a relationship between the measured observations and the sampling coordinates.   
     
     
         20 . The non-transitory computer readable medium according to  claim 19  wherein the model is a multi-exponential model. 
     
     
         21 . The non-transitory computer readable medium according to  claim 19  wherein the model is a diffusion weighted magnetic resonance imaging model. 
     
     
         22 . The non-transitory computer readable medium according to  claim 19  wherein the machine learning process is trained during a training period in which the machine learning process is fed by training observations and training sampling coordinates. 
     
     
         23 . The non-transitory computer readable medium according to  claim 19  wherein some of the training sampling coordinates are generating by randomly biasing initial training sampling coordinates to provide randomly biased training sampling coordinates. 
     
     
         24 . The non-transitory computer readable medium according to  claim 23  wherein some of the training observations represent estimated training observations obtained at the randomly biased trained sampling coordinates. 
     
     
         25 . The non-transitory computer readable medium according to  claim 23  wherein some of the training observations are simulated. 
     
     
         26 . The non-transitory computer readable medium according to  claim 19  that stores instructions for training the machine learning during a training period, wherein the training comprises feeding the machine learning process by training observations and training sampling coordinates. 
     
     
         27 . The non-transitory computer readable medium according to  claim 26  that stores instructions for generating some of the training sampling coordinates by randomly biasing initial training sampling coordinates to provide randomly biased training sampling coordinates. 
     
     
         28 . The non-transitory computer readable medium according to  claim 27  that stores instructions for obtaining some of the training observations at the randomly biased trained sampling coordinates. 
     
     
         29 . The non-transitory computer readable medium according to  claim 27  wherein some of the training observations are simulated. 
     
     
         30 . The non-transitory computer readable medium according to  claim 19  that stores instructions for feeding the measured observations and sampling coordinates of the measured observations to an input stage of the machine learning process. 
     
     
         31 . The non-transitory computer readable medium according to  claim 19  wherein the machine learning process is implemented by a neural network. 
     
     
         32 . The non-transitory computer readable medium according to  claim 31  wherein the neural network is a feed-forward back-propagation deep neural network. 
     
     
         33 . The non-transitory computer readable medium according to  claim 31  wherein the neural network comprises multiple fully connected layers. 
     
     
         34 . The method according to  claim 1  wherein the machine learning process is trained by a supervised training process. 
     
     
         35 . The non-transitory computer readable medium according to  claim 1  wherein the machine learning process is trained by an un-supervised training process. 
     
     
         36 . The non-transitory computer readable medium according to  claim 1  wherein the machine learning process is trained by a combination of a supervised training process and an un-supervised training process. 
     
     
         37 . A computerized system that comprises one or more processing circuits and a memory, wherein the one or more processing circuits are configured to:
 feed measured observations and sampling coordinates of the measured observations to a machine learning process; and   process the measured observations and the sampling coordinates of the measured observations, by the machine learning process, to provide an estimate of the parameters of the model; wherein the model is indicative of a relationship between the measured observations and the sampling coordinates, wherein the model is non-linear and is more complex than a log-linear model.